In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.

This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

Removal of Congo red, Rhodamine B, and Dispers Blue dyes from water solution have been achieved using Flint Clay as an adsorbent. The adsorption was studied as a function of contact time, adsorbent dose, pH, and temperature under batch adsorption technique. The equilibrium data fit with Langmuir, Freundlich and Toth models of adsorption and the linear regression coefficient R2 was used to elucidate the best fitting isotherm model. Different thermodynamic parameters, namely Gibb’s free energy, enthalpy and entropy of the on-going adsorption process have also been evaluated. Batch technique has been employed for the kinetic measurements and the adsorption of the three dyes follows a second order rate kinetics. The kinetic investigations al

Determining the aerodynamic characteristics of iced airfoil is an important step in aircraft design.  The goal of this work is to study experimentally and numerically an iced airfoil to assess the aerodynamic penalties associated with presence of ice on the airfoil surface. Three iced shapes were tested on NACA 0012 straight wing at zero and non-zero angles of attack, at Reynolds No. equal to (3.36*105). The 2-D steady state continuity and momentum equations have been solved utilizing finite volume method to analyze the turbulent flow over a clean and iced airfoil. The results show that the ice shapes affected the aerodynamic characteristics due to the change in airfoil shape. The experimental results show that the horn iced airfoil

      In this paper, a modified three-step iteration algorithm for approximating a joint fixed point of non-expansive and contraction mapping is studied. Under appropriate conditions, several strong convergence theorems and Δ-convergence theorems are established in a complete CAT (0) space. a numerical example is introduced to show that this modified iteration algorithm is faster than other iteration algorithms. Finally, we prove that the modified iteration algorithm is stable. Therefore these results are extended and improved to a novel results that are stated by other researchers. Our results are also complement to many well-known theorems in the literature. This type of research can be played a vital role in computer programming

A stochastic process {Xk, k = 1, 2, ...} is a doubly geometric stochastic process if there exists the ratio (a > 0) and the positive function (h(k) > 0), so that {α 1 h-k }; k ak X k = 1, 2, ... is a generalization of a geometric stochastic process. This process is stochastically monotone and can be used to model a point process with multiple trends. In this paper, we use nonparametric methods to investigate statistical inference for doubly geometric stochastic processes. A graphical technique for determining whether a process is in agreement with a doubly geometric stochastic process is proposed. Further, we can estimate the parameters a, b, μ and σ2 of the doubly geometric stochastic process by using the least squares estimate for Xk a

     Foreign Object Debris (FOD) is defined as one of the major problems in the airline maintenance industry, reducing the levels of safety. A foreign object which may result in causing serious damage to an airplane, including engine problems and personal safety risks. Therefore, it is critical to detect FOD in place to guarantee the safety of airplanes flying. FOD detection systems in the past lacked an effective method for automatic material recognition as well as high speed and accuracy in detecting materials. This paper proposes the FOD model using a variety of feature extraction approaches like Gray-level Co-occurrence Matrix (GLCM) and Linear Discriminant Analysis (LDA) to extract features and Deep Learning (DL) for classifi

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

The research presents the "theory of happiness according to Junaid al-Baghdadi" and the theory's most significant characteristics.

The reasons for happiness, include knowledge, love, and providence, and happiness itself is the return of man or spirit to the source from which it originated.